Realism of scenes involving water surfaces during rendering

ABSTRACT

A water surface mesh is determined for a scene to be rendered. This water surface mesh includes a grouping of geometric shapes such as triangles that represents the surface of the water. This water surface mesh is then used to create a refracted or reflected mesh. The refracted or reflected mesh shows an effect produced by the water surface&#39;s refraction or reflection of light. The relationship between the water surface mesh and the refracted or reflected mesh is then used to determine how to illuminate elements within the scene. This eliminates some previously necessary steps during rendering, and enables an accurate depiction of caustics within a scene that can be performed in real-time.

CLAIM OF PRIORITY

This application claims the benefit of U.S. Provisional Application No.62/658,534 (Attorney Docket No. 18-MU-0095US01) titled “METHODS ANDSYSTEMS FOR REFRACTED AND REFLECTED REAL-TIME CAUSTICS,” filed Apr. 16,2018, the entire contents of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to image rendering, and more particularlyto accounting for surface caustics during image rendering.

BACKGROUND

Water surface caustics (e.g., light patterns generated by lightrefracted or reflected off of a water surface within a scene, etc.)affect the way objects above and below a water source are illuminatedwithin a scene. Accounting for accurate water surface caustics duringrendering is time and resource-intensive, and cannot currently beaccurately performed in real-time. As a result, current real-timerenderings result in unrealistic water surface caustics within a scene.There is therefore a need to more efficiently address realistic watersurface caustics during rendering.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a flowchart of a method for improving realism ofscenes involving water surfaces during rendering, in accordance with anembodiment.

FIG. 2 illustrates a parallel processing unit, in accordance with anembodiment.

FIG. 3A illustrates a general processing cluster within the parallelprocessing unit of FIG. 2, in accordance with an embodiment.

FIG. 3B illustrates a memory partition unit of the parallel processingunit of FIG. 2, in accordance with an embodiment.

FIG. 4A illustrates the streaming multi-processor of FIG. 3A, inaccordance with an embodiment.

FIG. 4B is a conceptual diagram of a processing system implemented usingthe PPU of FIG. 2, in accordance with an embodiment.

FIG. 4C illustrates an exemplary system in which the variousarchitecture and/or functionality of the various previous embodimentsmay be implemented.

FIG. 5 is a conceptual diagram of a graphics processing pipelineimplemented by the PPU of FIG. 2, in accordance with an embodiment.

FIG. 6 illustrates a flowchart of a method for implementing real-timeray-traced water surface caustics, in accordance with one embodiment.

FIG. 7 illustrates an exemplary dynamic underwater three-dimensional(3D) scene, in accordance with one embodiment.

FIG. 8 illustrates an example of rendering raytraced water caustics, inaccordance with one embodiment.

FIG. 9 illustrates an exemplary refraction example, in accordance withone embodiment.

FIG. 10 illustrates an exemplary generation of samples and theircorresponding refracted screen space positions, in accordance with oneembodiment.

FIG. 11 illustrates an exemplary depiction of three triangles formed atthree different intersection points that three vertices/rays thatoriginate from the water surface generate, in accordance with oneembodiment.

DETAILED DESCRIPTION

In computer graphics, water surface caustics are light patternsgenerated by light refracted or reflected off of a water surface withina scene to be rendered. These water surface caustics affect the wayobjects above and below a water source are illuminated within a scene.Since accounting for these caustics is time and resource-intensive andcannot currently be accurately performed in real-time, real-timerenderings result in unrealistic water surface caustics within a scene.

To address this, a water surface mesh is determined for a scene to berendered. This water surface mesh is a grouping of geometric shapes suchas triangles that represents the surface of the water. This watersurface mesh is then used to create a lighting mesh, where the lightingmesh is a refracted or reflected mesh. The lighting mesh shows an effectproduced by the water surface's refraction or reflection of light. Therelationship between the water surface mesh and the lighting mesh isthen used to determine how to light elements within the scene. Thiseliminates some previously necessary steps during rendering, and enablesan accurate depiction of caustics within a scene that can be performedin real-time.

FIG. 1 illustrates a flowchart of a method 100 for improving a realismof scenes involving water surfaces during rendering, in accordance withan embodiment. Although method 100 is described in the context of aprocessing unit, the method 100 may also be performed by a program,custom circuitry, or by a combination of custom circuitry and a program.For example, the method 100 may be executed by a GPU (graphicsprocessing unit), CPU (central processing unit), or any processorcapable of performing parallel path space filtering by hashing.Furthermore, persons of ordinary skill in the art will understand thatany system that performs method 100 is within the scope and spirit ofembodiments of the present invention.

As shown in operation 102, a water surface mesh is determined for ascene to be rendered. In one embodiment, the water surface mesh includesa polygon mesh that represents a geometry of a water surface within thescene. In another embodiment, the water surface mesh includes aplurality of geometric instances (e.g., polygons such as triangles,etc.).

Additionally, as shown in operation 104, a ray is determined for eachvertex of the water surface mesh. In one embodiment, the ray starts at acurrent position of the vertex of the water surface mesh. In anotherembodiment, the ray may include a refracted ray that points along arefracted direction of incident light. In another embodiment, the raymay include a reflected ray that points along a reflected direction ofincident light. In still another embodiment, the ray is created by thelight source of the scene hitting the vertex of the water surface mesh.

Further, in one embodiment, the ray may include a refracted ray that iscreated by tracing rays from the light source and identifying arefraction of the rays at the vertices of the water surface mesh. Inanother embodiment, the ray may include a reflected ray that is createdby tracing rays from the light source and identifying a reflection ofthe rays at the vertices of the water surface mesh. In anotherembodiment, a direction of a refracted or reflected ray for a vertex ofthe water surface mesh is determined utilizing a surface normalcalculated for the vertex.

Further still, as shown in operation 106, a water mesh is computed forthe scene, utilizing the rays for each vertex of the water surface mesh.In one embodiment, the water mesh may include a refracted or reflectedwater mesh. In another embodiment, the water mesh has the same number ofvertices and the same polygon count as the water surface mesh. In yetanother embodiment, if the water mesh is a refracted water mesh, thepositions of the vertices within the refracted water mesh are determinedby intersecting each refracted ray with underwater geometry in the sceneto be rendered. In still another embodiment, if the water mesh is areflected water mesh, the positions of the vertices within the reflectedwater mesh are determined by intersecting each reflected ray withabove-water geometry in the scene to be rendered. In another embodiment,every polygon of the water surface mesh generates a correspondingpolygon in the refracted or reflected water mesh, based on thecorresponding refracted or reflected rays starting at vertices of thewater surface mesh.

Also, as shown in operation 108, a compression ratio is calculated foreach polygon of the water surface mesh. In one embodiment, thecompression ratio is computed based on the surface area of the polygonof the water surface mesh, and the surface area of the correspondingpolygon within the (refracted or reflected) water mesh. In anotherembodiment, the compression ratio for each polygon of the water surfacemesh may be stored within a buffer.

In addition, as shown in operation 110, light rays are projected fromone or more polygons of the water surface mesh onto scene geometry,based on the compression ratio computed for each polygon of the watersurface mesh. For example, if the water mesh is a refracted water mesh,refracted light rays are projected from one or more polygons of thewater surface mesh onto underwater scene geometry, based on thecompression ratio computed for each polygon of the water surface mesh.In another example, if the water mesh is a reflected water mesh,reflected light rays are projected from one or more polygons of thewater surface mesh onto above-water scene geometry, based on thecompression ratio computed for each polygon of the water surface mesh.In one embodiment, a number of refracted or reflected light raysprojected/generated from one or more polygons of the water surface meshmay be based on the compression ratio for the polygons and/or a screenspace size of the geometry of the water mesh.

Furthermore, in one embodiment, the compression ratio for a polygon ofthe water surface mesh may be compared to a predetermined threshold. Forexample, the predetermined threshold may have a value of one. In anotherembodiment, if the compression ratio does not exceed the threshold, thelight through the polygon is being diffused, and no light rays may beprojected/generated for the polygon of the water surface mesh.Alternately, a predetermined number of light rays may beprojected/generated for the polygon of the water surface mesh (where thenumber is lower than polygons having compression ratios greater than thethreshold).

Further still, in one embodiment, if the compression ratio exceeds thethreshold, the light through the polygon is being concentrated/focused,and light rays may be projected/generated for the polygon of the watersurface mesh. For example, the number of light rays that areprojected/generated may be proportional to the compression ratio for thepolygon. In another example, a first polygon with a first compressionratio may have more light rays projected/generated for the first polygonthan a second polygon with a second compression ration less than thefirst compression ratio.

Also, in one embodiment, a number of light rays projected/generated fromone or more polygons of the water surface mesh may be based on anon-screen size of corresponding polygons within the water mesh.

Additionally, in one embodiment, the light rays may beprojected/generated from random positions within each polygon of thewater surface mesh. For example, the random positions may be determinedutilizing a random number sequence that uses a unique per-polygon ID asa random seed value. For instance, each polygon of the water surfacemesh may be assigned a unique identifying number. In yet anotherexample, the identifying number may be used as a seed value to generaterandom numbers.

For instance, the identifying number may be input into a pseudo-randomnumber generator to generate a sequence of pseudo-random numbers. Thesame seed may always result in the same sequence of pseudo-randomnumbers from the pseudo-random number generator. This may ensure that asequence of random positions within the within the polygon is the sameeach time for that polygon over multiple scenes/frames, which maystabilize noise positions within the polygons of the water surface meshand may stabilize noise in general.

Further, in one embodiment, for each polygon of the water surface mesh,it may be determined whether each of the random positions determined forthat polygon are visible from the light source of the scene. Forexample, this may be performed by comparing the random positions to ashadow map for the scene, shooting a ray from the random positions tothe light source, etc.

Further still, in one embodiment, for each polygon of the water surfacemesh for which light rays are to be projected/generated, light rays areprojected/generated for each random position determined for that polygonthat are visible from the light source of the scene. For example, lightrays may be projected/generated by forming a ray (e.g., a photon, etc.)starting at each random position, along the interpolated refracted orreflected direction determined for the polygon.

Also, as shown in operation 112, lighting of the scene geometry isperformed, utilizing the projected light rays. In one embodiment, foreach polygon of the water surface mesh for which refracted light raysare to be projected/generated, an intersection of eachprojected/generated refracted light ray with underwater scene geometryis determined. In one embodiment, for each polygon of the water surfacemesh for which reflected light rays are to be projected/generated, anintersection of each projected/generated reflected light ray withabove-water scene geometry is determined. In another embodiment, eachintersection is projected to a screen space location (e.g., pixel). Forexample, the intersection point may be projected onto a two-dimensional(2D) position as seen by a point of view of a camera viewing the scene(the screen space location).

In addition, in one embodiment, if it is determined that the screenspace location is on-screen (e.g., visible on the screen, etc.), abrightness value for the screen space location is accumulated in abuffer. For example, for each pixel within the screen space, a screenspace buffer may store accumulated brightness (e.g., as a floating-pointvalue, etc.) from refracted rays for the pixel. In another example, theaccumulated brightness for a pixel may be scaled by one or more factors(e.g., the associated compression ratio for the polygon of the watersurface mesh, an amount of light absorbed by a length of the ray as ittravels through the water, etc.).

Furthermore, in one embodiment, the accumulated brightness value storedin the buffer for each screen space location may be denoised to create adenoised and smoothed caustics buffer value for the screen spacelocation. For example, denoising may be performed utilizing brightnessblurring. In another embodiment, denoised and smoothed caustics buffervalues for each screen space location (e.g., each pixel of the visiblescreen space) may be used to shed light onto the underwater orabove-water scene, thereby performing lighting of the underwater orabove-water scene geometry.

In this way, a refracted or reflected water mesh may act as a guidingmesh and may be used to determine a number and location of refracted orreflected rays to be projected/generated from a corresponding watersurface mesh of a scene. Additionally, the refracted or reflected raysmay be projected directly from the water surface mesh, instead of from alight source, which may eliminate a need for one or more intermediaterendering steps during rendering, which may improve a performance of oneor more computing devices performing the rendering. Also, projecting therefracted or reflected rays directly from the water surface mesh mayenable real-time ray tracing of the refracted or reflected rays toimplement water surface caustics (e.g., light patterns generated bylight refracted or reflected off of a water surface within a scene,etc.).

In yet another embodiment, the water mesh may be computed, and light rayprojection may be performed, utilizing a parallel processing unit (PPU)such as the PPU 200 illustrated in FIG. 2.

More illustrative information will now be set forth regarding variousoptional architectures and features with which the foregoing frameworkmay be implemented, per the desires of the user. It should be stronglynoted that the following information is set forth for illustrativepurposes and should not be construed as limiting in any manner. Any ofthe following features may be optionally incorporated with or withoutthe exclusion of other features described.

Parallel Processing Architecture

FIG. 2 illustrates a parallel processing unit (PPU) 200, in accordancewith an embodiment. In an embodiment, the PPU 200 is a multi-threadedprocessor that is implemented on one or more integrated circuit devices.The PPU 200 is a latency hiding architecture designed to process manythreads in parallel. A thread (i.e., a thread of execution) is aninstantiation of a set of instructions configured to be executed by thePPU 200. In an embodiment, the PPU 200 is a graphics processing unit(GPU) configured to implement a graphics rendering pipeline forprocessing three-dimensional (3D) graphics data in order to generatetwo-dimensional (2D) image data for display on a display device such asa liquid crystal display (LCD) device. In other embodiments, the PPU 200may be utilized for performing general-purpose computations. While oneexemplary parallel processor is provided herein for illustrativepurposes, it should be strongly noted that such processor is set forthfor illustrative purposes only, and that any processor may be employedto supplement and/or substitute for the same.

One or more PPUs 200 may be configured to accelerate thousands of HighPerformance Computing (HPC), data center, and machine learningapplications. The PPU 200 may be configured to accelerate numerous deeplearning systems and applications including autonomous vehicleplatforms, deep learning, high-accuracy speech, image, and textrecognition systems, intelligent video analytics, molecular simulations,drug discovery, disease diagnosis, weather forecasting, big dataanalytics, astronomy, molecular dynamics simulation, financial modeling,robotics, factory automation, real-time language translation, onlinesearch optimizations, and personalized user recommendations, and thelike.

As shown in FIG. 2, the PPU 200 includes an Input/Output (I/O) unit 205,a front end unit 215, a scheduler unit 220, a work distribution unit225, a hub 230, a crossbar (Xbar) 270, one or more general processingclusters (GPCs) 250, and one or more partition units 280. The PPU 200may be connected to a host processor or other PPUs 200 via one or morehigh-speed NVLink 210 interconnect. The PPU 200 may be connected to ahost processor or other peripheral devices via an interconnect 202. ThePPU 200 may also be connected to a local memory comprising a number ofmemory devices 204. In an embodiment, the local memory may comprise anumber of dynamic random access memory (DRAM) devices. The DRAM devicesmay be configured as a high-bandwidth memory (HBM) subsystem, withmultiple DRAM dies stacked within each device.

The NVLink 210 interconnect enables systems to scale and include one ormore PPUs 200 combined with one or more CPUs, supports cache coherencebetween the PPUs 200 and CPUs, and CPU mastering. Data and/or commandsmay be transmitted by the NVLink 210 through the hub 230 to/from otherunits of the PPU 200 such as one or more copy engines, a video encoder,a video decoder, a power management unit, etc. (not explicitly shown).The NVLink 210 is described in more detail in conjunction with FIG. 4B.

The I/O unit 205 is configured to transmit and receive communications(i.e., commands, data, etc.) from a host processor (not shown) over theinterconnect 202. The I/O unit 205 may communicate with the hostprocessor directly via the interconnect 202 or through one or moreintermediate devices such as a memory bridge. In an embodiment, the I/Ounit 205 may communicate with one or more other processors, such as oneor more the PPUs 200 via the interconnect 202. In an embodiment, the I/Ounit 205 implements a Peripheral Component Interconnect Express (PCIe)interface for communications over a PCIe bus and the interconnect 202 isa PCIe bus. In alternative embodiments, the I/O unit 205 may implementother types of well-known interfaces for communicating with externaldevices.

The I/O unit 205 decodes packets received via the interconnect 202. Inan embodiment, the packets represent commands configured to cause thePPU 200 to perform various operations. The I/O unit 205 transmits thedecoded commands to various other units of the PPU 200 as the commandsmay specify. For example, some commands may be transmitted to the frontend unit 215. Other commands may be transmitted to the hub 230 or otherunits of the PPU 200 such as one or more copy engines, a video encoder,a video decoder, a power management unit, etc. (not explicitly shown).In other words, the I/O unit 205 is configured to route communicationsbetween and among the various logical units of the PPU 200.

In an embodiment, a program executed by the host processor encodes acommand stream in a buffer that provides workloads to the PPU 200 forprocessing. A workload may comprise several instructions and data to beprocessed by those instructions. The buffer is a region in a memory thatis accessible (i.e., read/write) by both the host processor and the PPU200. For example, the I/O unit 205 may be configured to access thebuffer in a system memory connected to the interconnect 202 via memoryrequests transmitted over the interconnect 202. In an embodiment, thehost processor writes the command stream to the buffer and thentransmits a pointer to the start of the command stream to the PPU 200.The front end unit 215 receives pointers to one or more command streams.The front end unit 215 manages the one or more streams, reading commandsfrom the streams and forwarding commands to the various units of the PPU200.

The front end unit 215 is coupled to a scheduler unit 220 thatconfigures the various GPCs 250 to process tasks defined by the one ormore streams. The scheduler unit 220 is configured to track stateinformation related to the various tasks managed by the scheduler unit220. The state may indicate which GPC 250 a task is assigned to, whetherthe task is active or inactive, a priority level associated with thetask, and so forth. The scheduler unit 220 manages the execution of aplurality of tasks on the one or more GPCs 250.

The scheduler unit 220 is coupled to a work distribution unit 225 thatis configured to dispatch tasks for execution on the GPCs 250. The workdistribution unit 225 may track a number of scheduled tasks receivedfrom the scheduler unit 220. In an embodiment, the work distributionunit 225 manages a pending task pool and an active task pool for each ofthe GPCs 250. The pending task pool may comprise a number of slots(e.g., 32 slots) that contain tasks assigned to be processed by aparticular GPC 250. The active task pool may comprise a number of slots(e.g., 4 slots) for tasks that are actively being processed by the GPCs250. As a GPC 250 finishes the execution of a task, that task is evictedfrom the active task pool for the GPC 250 and one of the other tasksfrom the pending task pool is selected and scheduled for execution onthe GPC 250. If an active task has been idle on the GPC 250, such aswhile waiting for a data dependency to be resolved, then the active taskmay be evicted from the GPC 250 and returned to the pending task poolwhile another task in the pending task pool is selected and scheduledfor execution on the GPC 250.

The work distribution unit 225 communicates with the one or more GPCs250 via XBar 270. The XBar 270 is an interconnect network that couplesmany of the units of the PPU 200 to other units of the PPU 200. Forexample, the XBar 270 may be configured to couple the work distributionunit 225 to a particular GPC 250. Although not shown explicitly, one ormore other units of the PPU 200 may also be connected to the XBar 270via the hub 230.

The tasks are managed by the scheduler unit 220 and dispatched to a GPC250 by the work distribution unit 225. The GPC 250 is configured toprocess the task and generate results. The results may be consumed byother tasks within the GPC 250, routed to a different GPC 250 via theXBar 270, or stored in the memory 204. The results can be written to thememory 204 via the partition units 280, which implement a memoryinterface for reading and writing data to/from the memory 204. Theresults can be transmitted to another PPU 200 or CPU via the NVLink 210.In an embodiment, the PPU 200 includes a number U of partition units 280that is equal to the number of separate and distinct memory devices 204coupled to the PPU 200. A partition unit 280 will be described in moredetail below in conjunction with FIG. 3B.

In an embodiment, a host processor executes a driver kernel thatimplements an application programming interface (API) that enables oneor more applications executing on the host processor to scheduleoperations for execution on the PPU 200. In an embodiment, multiplecompute applications are simultaneously executed by the PPU 200 and thePPU 200 provides isolation, quality of service (QoS), and independentaddress spaces for the multiple compute applications. An application maygenerate instructions (i.e., API calls) that cause the driver kernel togenerate one or more tasks for execution by the PPU 200. The driverkernel outputs tasks to one or more streams being processed by the PPU200. Each task may comprise one or more groups of related threads,referred to herein as a warp. In an embodiment, a warp comprises 32related threads that may be executed in parallel. Cooperating threadsmay refer to a plurality of threads including instructions to performthe task and that may exchange data through shared memory. Threads andcooperating threads are described in more detail in conjunction withFIG. 4A.

FIG. 3A illustrates a GPC 250 of the PPU 200 of FIG. 2, in accordancewith an embodiment. As shown in FIG. 3A, each GPC 250 includes a numberof hardware units for processing tasks. In an embodiment, each GPC 250includes a pipeline manager 310, a pre-raster operations unit (PROP)315, a raster engine 325, a work distribution crossbar (WDX) 380, amemory management unit (MMU) 390, and one or more Data ProcessingClusters (DPCs) 320. It will be appreciated that the GPC 250 of FIG. 3Amay include other hardware units in lieu of or in addition to the unitsshown in FIG. 3A.

In an embodiment, the operation of the GPC 250 is controlled by thepipeline manager 310. The pipeline manager 310 manages the configurationof the one or more DPCs 320 for processing tasks allocated to the GPC250. In an embodiment, the pipeline manager 310 may configure at leastone of the one or more DPCs 320 to implement at least a portion of agraphics rendering pipeline. For example, a DPC 320 may be configured toexecute a vertex shader program on the programmable streamingmultiprocessor (SM) 340. The pipeline manager 310 may also be configuredto route packets received from the work distribution unit 225 to theappropriate logical units within the GPC 250. For example, some packetsmay be routed to fixed function hardware units in the PROP 315 and/orraster engine 325 while other packets may be routed to the DPCs 320 forprocessing by the primitive engine 335 or the SM 340. In an embodiment,the pipeline manager 310 may configure at least one of the one or moreDPCs 320 to implement a neural network model and/or a computingpipeline.

The PROP unit 315 is configured to route data generated by the rasterengine 325 and the DPCs 320 to a Raster Operations (ROP) unit, describedin more detail in conjunction with FIG. 3B. The PROP unit 315 may alsobe configured to perform optimizations for color blending, organizepixel data, perform address translations, and the like.

The raster engine 325 includes a number of fixed function hardware unitsconfigured to perform various raster operations. In an embodiment, theraster engine 325 includes a setup engine, a coarse raster engine, aculling engine, a clipping engine, a fine raster engine, and a tilecoalescing engine. The setup engine receives transformed vertices andgenerates plane equations associated with the geometric primitivedefined by the vertices. The plane equations are transmitted to thecoarse raster engine to generate coverage information (e.g., an x,ycoverage mask for a tile) for the primitive. The output of the coarseraster engine is transmitted to the culling engine where fragmentsassociated with the primitive that fail a z-test are culled, andtransmitted to a clipping engine where fragments lying outside a viewingfrustum are clipped. Those fragments that survive clipping and cullingmay be passed to the fine raster engine to generate attributes for thepixel fragments based on the plane equations generated by the setupengine. The output of the raster engine 325 comprises fragments to beprocessed, for example, by a fragment shader implemented within a DPC320.

Each DPC 320 included in the GPC 250 includes an M-Pipe Controller (MPC)330, a primitive engine 335, and one or more SMs 340. The MPC 330controls the operation of the DPC 320, routing packets received from thepipeline manager 310 to the appropriate units in the DPC 320. Forexample, packets associated with a vertex may be routed to the primitiveengine 335, which is configured to fetch vertex attributes associatedwith the vertex from the memory 204. In contrast, packets associatedwith a shader program may be transmitted to the SM 340.

The SM 340 comprises a programmable streaming processor that isconfigured to process tasks represented by a number of threads. Each SM340 is multi-threaded and configured to execute a plurality of threads(e.g., 32 threads) from a particular group of threads concurrently. Inan embodiment, the SM 340 implements a SIMD (Single-Instruction,Multiple-Data) architecture where each thread in a group of threads(i.e., a warp) is configured to process a different set of data based onthe same set of instructions. All threads in the group of threadsexecute the same instructions. In another embodiment, the SM 340implements a SIMT (Single-Instruction, Multiple Thread) architecturewhere each thread in a group of threads is configured to process adifferent set of data based on the same set of instructions, but whereindividual threads in the group of threads are allowed to diverge duringexecution. In an embodiment, a program counter, call stack, andexecution state is maintained for each warp, enabling concurrencybetween warps and serial execution within warps when threads within thewarp diverge. In another embodiment, a program counter, call stack, andexecution state is maintained for each individual thread, enabling equalconcurrency between all threads, within and between warps. Whenexecution state is maintained for each individual thread, threadsexecuting the same instructions may be converged and executed inparallel for maximum efficiency. The SM 340 will be described in moredetail below in conjunction with FIG. 4A.

The MMU 390 provides an interface between the GPC 250 and the partitionunit 280. The MMU 390 may provide translation of virtual addresses intophysical addresses, memory protection, and arbitration of memoryrequests. In an embodiment, the MMU 390 provides one or more translationlookaside buffers (TLBs) for performing translation of virtual addressesinto physical addresses in the memory 204.

FIG. 3B illustrates a memory partition unit 280 of the PPU 200 of FIG.2, in accordance with an embodiment. As shown in FIG. 3B, the memorypartition unit 280 includes a Raster Operations (ROP) unit 350, a leveltwo (L2) cache 360, and a memory interface 370. The memory interface 370is coupled to the memory 204. Memory interface 370 may implement 32, 64,128, 1024-bit data buses, or the like, for high-speed data transfer. Inan embodiment, the PPU 200 incorporates U memory interfaces 370, onememory interface 370 per pair of partition units 280, where each pair ofpartition units 280 is connected to a corresponding memory device 204.For example, PPU 200 may be connected to up to Y memory devices 204,such as high bandwidth memory stacks or graphics double-data-rate,version 5, synchronous dynamic random access memory, or other types ofpersistent storage.

In an embodiment, the memory interface 370 implements an HBM2 memoryinterface and Y equals half U. In an embodiment, the HBM2 memory stacksare located on the same physical package as the PPU 200, providingsubstantial power and area savings compared with conventional GDDR5SDRAM systems. In an embodiment, each HBM2 stack includes four memorydies and Y equals 4, with HBM2 stack including two 128-bit channels perdie for a total of 8 channels and a data bus width of 1024 bits.

In an embodiment, the memory 204 supports Single-Error CorrectingDouble-Error Detecting (SECDED) Error Correction Code (ECC) to protectdata. ECC provides higher reliability for compute applications that aresensitive to data corruption. Reliability is especially important inlarge-scale cluster computing environments where PPUs 200 process verylarge datasets and/or run applications for extended periods.

In an embodiment, the PPU 200 implements a multi-level memory hierarchy.In an embodiment, the memory partition unit 280 supports a unifiedmemory to provide a single unified virtual address space for CPU and PPU200 memory, enabling data sharing between virtual memory systems. In anembodiment the frequency of accesses by a PPU 200 to memory located onother processors is traced to ensure that memory pages are moved to thephysical memory of the PPU 200 that is accessing the pages morefrequently. In an embodiment, the NVLink 210 supports addresstranslation services allowing the PPU 200 to directly access a CPU'spage tables and providing full access to CPU memory by the PPU 200.

In an embodiment, copy engines transfer data between multiple PPUs 200or between PPUs 200 and CPUs. The copy engines can generate page faultsfor addresses that are not mapped into the page tables. The memorypartition unit 280 can then service the page faults, mapping theaddresses into the page table, after which the copy engine can performthe transfer. In a conventional system, memory is pinned (i.e.,non-pageable) for multiple copy engine operations between multipleprocessors, substantially reducing the available memory. With hardwarepage faulting, addresses can be passed to the copy engines withoutworrying if the memory pages are resident, and the copy process istransparent.

Data from the memory 204 or other system memory may be fetched by thememory partition unit 280 and stored in the L2 cache 360, which islocated on-chip and is shared between the various GPCs 250. As shown,each memory partition unit 280 includes a portion of the L2 cache 360associated with a corresponding memory device 204. Lower level cachesmay then be implemented in various units within the GPCs 250. Forexample, each of the SMs 340 may implement a level one (L1) cache. TheL1 cache is private memory that is dedicated to a particular SM 340.Data from the L2 cache 360 may be fetched and stored in each of the L1caches for processing in the functional units of the SMs 340. The L2cache 360 is coupled to the memory interface 370 and the XBar 270.

The ROP unit 350 performs graphics raster operations related to pixelcolor, such as color compression, pixel blending, and the like. The ROPunit 350 also implements depth testing in conjunction with the rasterengine 325, receiving a depth for a sample location associated with apixel fragment from the culling engine of the raster engine 325. Thedepth is tested against a corresponding depth in a depth buffer for asample location associated with the fragment. If the fragment passes thedepth test for the sample location, then the ROP unit 350 updates thedepth buffer and transmits a result of the depth test to the rasterengine 325. It will be appreciated that the number of partition units280 may be different than the number of GPCs 250 and, therefore, eachROP unit 350 may be coupled to each of the GPCs 250. The ROP unit 350tracks packets received from the different GPCs 250 and determines whichGPC 250 that a result generated by the ROP unit 350 is routed to throughthe Xbar 270. Although the ROP unit 350 is included within the memorypartition unit 280 in FIG. 3B, in other embodiment, the ROP unit 350 maybe outside of the memory partition unit 280. For example, the ROP unit350 may reside in the GPC 250 or another unit.

FIG. 4A illustrates the streaming multi-processor 340 of FIG. 3A, inaccordance with an embodiment. As shown in FIG. 4A, the SM 340 includesan instruction cache 405, one or more scheduler units 410(K), a registerfile 420, one or more processing cores 450, one or more special functionunits (SFUs) 452, one or more load/store units (LSUs) 454, aninterconnect network 480, a shared memory/L1 cache 470.

As described above, the work distribution unit 225 dispatches tasks forexecution on the GPCs 250 of the PPU 200. The tasks are allocated to aparticular DPC 320 within a GPC 250 and, if the task is associated witha shader program, the task may be allocated to an SM 340. The schedulerunit 410(K) receives the tasks from the work distribution unit 225 andmanages instruction scheduling for one or more thread blocks assigned tothe SM 340. The scheduler unit 410(K) schedules thread blocks forexecution as warps of parallel threads, where each thread block isallocated at least one warp. In an embodiment, each warp executes 32threads. The scheduler unit 410(K) may manage a plurality of differentthread blocks, allocating the warps to the different thread blocks andthen dispatching instructions from the plurality of differentcooperative groups to the various functional units (i.e., cores 450,SFUs 452, and LSUs 454) during each clock cycle.

Cooperative Groups is a programming model for organizing groups ofcommunicating threads that allows developers to express the granularityat which threads are communicating, enabling the expression of richer,more efficient parallel decompositions. Cooperative launch APIs supportsynchronization amongst thread blocks for the execution of parallelalgorithms. Conventional programming models provide a single, simpleconstruct for synchronizing cooperating threads: a barrier across allthreads of a thread block (i.e., the syncthreads( ) function). However,programmers would often like to define groups of threads at smaller thanthread block granularities and synchronize within the defined groups toenable greater performance, design flexibility, and software reuse inthe form of collective group-wide function interfaces.

Cooperative Groups enables programmers to define groups of threadsexplicitly at sub-block (i.e., as small as a single thread) andmulti-block granularities, and to perform collective operations such assynchronization on the threads in a cooperative group. The programmingmodel supports clean composition across software boundaries, so thatlibraries and utility functions can synchronize safely within theirlocal context without having to make assumptions about convergence.Cooperative Groups primitives enable new patterns of cooperativeparallelism, including producer-consumer parallelism, opportunisticparallelism, and global synchronization across an entire grid of threadblocks.

A dispatch unit 415 is configured to transmit instructions to one ormore of the functional units. In the embodiment, the scheduler unit410(K) includes two dispatch units 415 that enable two differentinstructions from the same warp to be dispatched during each clockcycle. In alternative embodiments, each scheduler unit 410(K) mayinclude a single dispatch unit 415 or additional dispatch units 415.

Each SM 340 includes a register file 420 that provides a set ofregisters for the functional units of the SM 340. In an embodiment, theregister file 420 is divided between each of the functional units suchthat each functional unit is allocated a dedicated portion of theregister file 420. In another embodiment, the register file 420 isdivided between the different warps being executed by the SM 340. Theregister file 420 provides temporary storage for operands connected tothe data paths of the functional units.

Each SM 340 comprises L processing cores 450. In an embodiment, the SM340 includes a large number (e.g., 128, etc.) of distinct processingcores 450. Each core 450 may include a fully-pipelined,single-precision, double-precision, and/or mixed precision processingunit that includes a floating point arithmetic logic unit and an integerarithmetic logic unit. In an embodiment, the floating point arithmeticlogic units implement the IEEE 754-2008 standard for floating pointarithmetic. In an embodiment, the cores 450 include 64 single-precision(32-bit) floating point cores, 64 integer cores, 32 double-precision(64-bit) floating point cores, and 8 tensor cores.

Tensor cores configured to perform matrix operations, and, in anembodiment, one or more tensor cores are included in the cores 450. Inparticular, the tensor cores are configured to perform deep learningmatrix arithmetic, such as convolution operations for neural networktraining and inferencing. In an embodiment, each tensor core operates ona 4×4 matrix and performs a matrix multiply and accumulate operationD=A×B+C, where A, B, C, and D are 4×4 matrices.

In an embodiment, the matrix multiply inputs A and B are 16-bit floatingpoint matrices, while the accumulation matrices C and D may be 16-bitfloating point or 32-bit floating point matrices. Tensor Cores operateon 16-bit floating point input data with 32-bit floating pointaccumulation. The 16-bit floating point multiply requires 64 operationsand results in a full precision product that is then accumulated using32-bit floating point addition with the other intermediate products fora 4×4×4 matrix multiply. In practice, Tensor Cores are used to performmuch larger two-dimensional or higher dimensional matrix operations,built up from these smaller elements. An API, such as CUDA 9 C++ API,exposes specialized matrix load, matrix multiply and accumulate, andmatrix store operations to efficiently use Tensor Cores from a CUDA-C++program. At the CUDA level, the warp-level interface assumes 16×16 sizematrices spanning all 32 threads of the warp.

Each SM 340 also comprises M SFUs 452 that perform special functions(e.g., attribute evaluation, reciprocal square root, and the like). Inan embodiment, the SFUs 452 may include a tree traversal unit configuredto traverse a hierarchical tree data structure. In an embodiment, theSFUs 452 may include texture unit configured to perform texture mapfiltering operations. In an embodiment, the texture units are configuredto load texture maps (e.g., a 2D array of texels) from the memory 204and sample the texture maps to produce sampled texture values for use inshader programs executed by the SM 340. In an embodiment, the texturemaps are stored in the shared memory/L1 cache 370. The texture unitsimplement texture operations such as filtering operations using mip-maps(i.e., texture maps of varying levels of detail). In an embodiment, eachSM 240 includes two texture units.

Each SM 340 also comprises N LSUs 454 that implement load and storeoperations between the shared memory/L1 cache 470 and the register file420. Each SM 340 includes an interconnect network 480 that connects eachof the functional units to the register file 420 and the LSU 454 to theregister file 420, shared memory/L1 cache 470. In an embodiment, theinterconnect network 480 is a crossbar that can be configured to connectany of the functional units to any of the registers in the register file420 and connect the LSUs 454 to the register file and memory locationsin shared memory/L1 cache 470.

The shared memory/L1 cache 470 is an array of on-chip memory that allowsfor data storage and communication between the SM 340 and the primitiveengine 335 and between threads in the SM 340. In an embodiment, theshared memory/L1 cache 470 comprises 128 KB of storage capacity and isin the path from the SM 340 to the partition unit 280. The sharedmemory/L1 cache 470 can be used to cache reads and writes. One or moreof the shared memory/L1 cache 470, L2 cache 360, and memory 204 arebacking stores.

Combining data cache and shared memory functionality into a singlememory block provides the best overall performance for both types ofmemory accesses. The capacity is usable as a cache by programs that donot use shared memory. For example, if shared memory is configured touse half of the capacity, texture and load/store operations can use theremaining capacity. Integration within the shared memory/L1 cache 470enables the shared memory/L1 cache 470 to function as a high-throughputconduit for streaming data while simultaneously providing high-bandwidthand low-latency access to frequently reused data.

When configured for general purpose parallel computation, a simplerconfiguration can be used compared with graphics processing.Specifically, the fixed function graphics processing units shown in FIG.2, are bypassed, creating a much simpler programming model. In thegeneral purpose parallel computation configuration, the workdistribution unit 225 assigns and distributes blocks of threads directlyto the DPCs 320. The threads in a block execute the same program, usinga unique thread ID in the calculation to ensure each thread generatesunique results, using the SM 340 to execute the program and performcalculations, shared memory/L1 cache 470 to communicate between threads,and the LSU 454 to read and write global memory through the sharedmemory/L1 cache 470 and the memory partition unit 280. When configuredfor general purpose parallel computation, the SM 340 can also writecommands that the scheduler unit 220 can use to launch new work on theDPCs 320.

The PPU 200 may be included in a desktop computer, a laptop computer, atablet computer, servers, supercomputers, a smart-phone (e.g., awireless, hand-held device), personal digital assistant (PDA), a digitalcamera, a vehicle, a head mounted display, a hand-held electronicdevice, and the like. In an embodiment, the PPU 200 is embodied on asingle semiconductor substrate. In another embodiment, the PPU 200 isincluded in a system-on-a-chip (SoC) along with one or more otherdevices such as additional PPUs 200, the memory 204, a reducedinstruction set computer (RISC) CPU, a memory management unit (MMU), adigital-to-analog converter (DAC), and the like.

In an embodiment, the PPU 200 may be included on a graphics card thatincludes one or more memory devices 204. The graphics card may beconfigured to interface with a PCIe slot on a motherboard of a desktopcomputer. In yet another embodiment, the PPU 200 may be an integratedgraphics processing unit (iGPU) or parallel processor included in thechipset of the motherboard.

Exemplary Computing System

Systems with multiple GPUs and CPUs are used in a variety of industriesas developers expose and leverage more parallelism in applications suchas artificial intelligence computing. High-performance GPU-acceleratedsystems with tens to many thousands of compute nodes are deployed indata centers, research facilities, and supercomputers to solve everlarger problems. As the number of processing devices within thehigh-performance systems increases, the communication and data transfermechanisms need to scale to support the increased bandwidth.

FIG. 4B is a conceptual diagram of a processing system 400 implementedusing the PPU 200 of FIG. 2, in accordance with an embodiment. Theexemplary system 465 may be configured to implement the method 100 shownin FIG. 1. The processing system 400 includes a CPU 430, switch 410, andmultiple PPUs 200 each and respective memories 204. The NVLink 210provides high-speed communication links between each of the PPUs 200.Although a particular number of NVLink 210 and interconnect 202connections are illustrated in FIG. 4B, the number of connections toeach PPU 200 and the CPU 430 may vary. The switch 410 interfaces betweenthe interconnect 202 and the CPU 430. The PPUs 200, memories 204, andNVLinks 210 may be situated on a single semiconductor platform to form aparallel processing module 425. In an embodiment, the switch 410supports two or more protocols to interface between various differentconnections and/or links.

In another embodiment (not shown), the NVLink 210 provides one or morehigh-speed communication links between each of the PPUs 200 and the CPU430 and the switch 410 interfaces between the interconnect 202 and eachof the PPUs 200. The PPUs 200, memories 204, and interconnect 202 may besituated on a single semiconductor platform to form a parallelprocessing module 425. In yet another embodiment (not shown), theinterconnect 202 provides one or more communication links between eachof the PPUs 200 and the CPU 430 and the switch 410 interfaces betweeneach of the PPUs 200 using the NVLink 210 to provide one or morehigh-speed communication links between the PPUs 200. In anotherembodiment (not shown), the NVLink 210 provides one or more high-speedcommunication links between the PPUs 200 and the CPU 430 through theswitch 410. In yet another embodiment (not shown), the interconnect 202provides one or more communication links between each of the PPUs 200directly. One or more of the NVLink 210 high-speed communication linksmay be implemented as a physical NVLink interconnect or either anon-chip or on-die interconnect using the same protocol as the NVLink210.

In the context of the present description, a single semiconductorplatform may refer to a sole unitary semiconductor-based integratedcircuit fabricated on a die or chip. It should be noted that the termsingle semiconductor platform may also refer to multi-chip modules withincreased connectivity which simulate on-chip operation and makesubstantial improvements over utilizing a conventional busimplementation. Of course, the various circuits or devices may also besituated separately or in various combinations of semiconductorplatforms per the desires of the user. Alternately, the parallelprocessing module 425 may be implemented as a circuit board substrateand each of the PPUs 200 and/or memories 204 may be packaged devices. Inan embodiment, the CPU 430, switch 410, and the parallel processingmodule 425 are situated on a single semiconductor platform.

In an embodiment, the signaling rate of each NVLink 210 is 20 to 25Gigabits/second and each PPU 200 includes six NVLink 210 interfaces (asshown in FIG. 4B, five NVLink 210 interfaces are included for each PPU200). Each NVLink 210 provides a data transfer rate of 25Gigabytes/second in each direction, with six links providing 300Gigabytes/second. The NVLinks 210 can be used exclusively for PPU-to-PPUcommunication as shown in FIG. 4B, or some combination of PPU-to-PPU andPPU-to-CPU, when the CPU 430 also includes one or more NVLink 210interfaces.

In an embodiment, the NVLink 210 allows direct load/store/atomic accessfrom the CPU 430 to each PPU's 200 memory 204. In an embodiment, theNVLink 210 supports coherency operations, allowing data read from thememories 204 to be stored in the cache hierarchy of the CPU 430,reducing cache access latency for the CPU 430. In an embodiment, theNVLink 210 includes support for Address Translation Services (ATS),allowing the PPU 200 to directly access page tables within the CPU 430.One or more of the NVLinks 210 may also be configured to operate in alow-power mode.

FIG. 4C illustrates an exemplary system 465 in which the variousarchitecture and/or functionality of the various previous embodimentsmay be implemented. The exemplary system 465 may be configured toimplement the method 100 shown in FIG. 1.

As shown, a system 465 is provided including at least one centralprocessing unit 430 that is connected to a communication bus 475. Thecommunication bus 475 may be implemented using any suitable protocol,such as PCI (Peripheral Component Interconnect), PCI-Express, AGP(Accelerated Graphics Port), HyperTransport, or any other bus orpoint-to-point communication protocol(s). The system 465 also includes amain memory 440. Control logic (software) and data are stored in themain memory 440 which may take the form of random access memory (RAM).

The system 465 also includes input devices 460, the parallel processingsystem 425, and display devices 445, i.e. a conventional CRT (cathoderay tube), LCD (liquid crystal display), LED (light emitting diode),plasma display or the like. User input may be received from the inputdevices 460, e.g., keyboard, mouse, touchpad, microphone, and the like.Each of the foregoing modules and/or devices may even be situated on asingle semiconductor platform to form the system 465. Alternately, thevarious modules may also be situated separately or in variouscombinations of semiconductor platforms per the desires of the user.

Further, the system 465 may be coupled to a network (e.g., atelecommunications network, local area network (LAN), wireless network,wide area network (WAN) such as the Internet, peer-to-peer network,cable network, or the like) through a network interface 435 forcommunication purposes.

The system 465 may also include a secondary storage (not shown). Thesecondary storage includes, for example, a hard disk drive and/or aremovable storage drive, representing a floppy disk drive, a magnetictape drive, a compact disk drive, digital versatile disk (DVD) drive,recording device, universal serial bus (USB) flash memory. The removablestorage drive reads from and/or writes to a removable storage unit in awell-known manner.

Computer programs, or computer control logic algorithms, may be storedin the main memory 440 and/or the secondary storage. Such computerprograms, when executed, enable the system 465 to perform variousfunctions. The memory 440, the storage, and/or any other storage arepossible examples of computer-readable media.

The architecture and/or functionality of the various previous figuresmay be implemented in the context of a general computer system, acircuit board system, a game console system dedicated for entertainmentpurposes, an application-specific system, and/or any other desiredsystem. For example, the system 465 may take the form of a desktopcomputer, a laptop computer, a tablet computer, servers, supercomputers,a smart-phone (e.g., a wireless, hand-held device), personal digitalassistant (PDA), a digital camera, a vehicle, a head mounted display, ahand-held electronic device, a mobile phone device, a television,workstation, game consoles, embedded system, and/or any other type oflogic.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Thus, the breadth and scope of a preferred embodiment shouldnot be limited by any of the above-described exemplary embodiments, butshould be defined only in accordance with the following claims and theirequivalents.

Graphics Processing Pipeline

In an embodiment, the PPU 200 comprises a graphics processing unit(GPU). The PPU 200 is configured to receive commands that specify shaderprograms for processing graphics data. Graphics data may be defined as aset of primitives such as points, lines, triangles, quads, trianglestrips, and the like. Typically, a primitive includes data thatspecifies a number of vertices for the primitive (e.g., in a model-spacecoordinate system) as well as attributes associated with each vertex ofthe primitive. The PPU 200 can be configured to process the graphicsprimitives to generate a frame buffer (i.e., pixel data for each of thepixels of the display).

An application writes model data for a scene (i.e., a collection ofvertices and attributes) to a memory such as a system memory or memory204. The model data defines each of the objects that may be visible on adisplay. The application then makes an API call to the driver kernelthat requests the model data to be rendered and displayed. The driverkernel reads the model data and writes commands to the one or morestreams to perform operations to process the model data. The commandsmay reference different shader programs to be implemented on the SMs 340of the PPU 200 including one or more of a vertex shader, hull shader,domain shader, geometry shader, and a pixel shader. For example, one ormore of the SMs 340 may be configured to execute a vertex shader programthat processes a number of vertices defined by the model data. In anembodiment, the different SMs 340 may be configured to execute differentshader programs concurrently. For example, a first subset of SMs 340 maybe configured to execute a vertex shader program while a second subsetof SMs 340 may be configured to execute a pixel shader program. Thefirst subset of SMs 340 processes vertex data to produce processedvertex data and writes the processed vertex data to the L2 cache 360and/or the memory 204. After the processed vertex data is rasterized(i.e., transformed from three-dimensional data into two-dimensional datain screen space) to produce fragment data, the second subset of SMs 340executes a pixel shader to produce processed fragment data, which isthen blended with other processed fragment data and written to the framebuffer in memory 204. The vertex shader program and pixel shader programmay execute concurrently, processing different data from the same scenein a pipelined fashion until all of the model data for the scene hasbeen rendered to the frame buffer. Then, the contents of the framebuffer are transmitted to a display controller for display on a displaydevice.

FIG. 5 is a conceptual diagram of a graphics processing pipeline 500implemented by the PPU 200 of FIG. 2, in accordance with an embodiment.The graphics processing pipeline 500 is an abstract flow diagram of theprocessing steps implemented to generate 2D computer-generated imagesfrom 3D geometry data. As is well-known, pipeline architectures mayperform long latency operations more efficiently by splitting up theoperation into a plurality of stages, where the output of each stage iscoupled to the input of the next successive stage. Thus, the graphicsprocessing pipeline 500 receives input data 501 that is transmitted fromone stage to the next stage of the graphics processing pipeline 500 togenerate output data 502. In an embodiment, the graphics processingpipeline 500 may represent a graphics processing pipeline defined by theOpenGL® API. As an option, the graphics processing pipeline 500 may beimplemented in the context of the functionality and architecture of theprevious Figures and/or any subsequent Figure(s).

As shown in FIG. 5, the graphics processing pipeline 500 comprises apipeline architecture that includes a number of stages. The stagesinclude, but are not limited to, a data assembly stage 510, a vertexshading stage 520, a primitive assembly stage 530, a geometry shadingstage 540, a viewport scale, cull, and clip (VSCC) stage 550, arasterization stage 560, a fragment shading stage 570, and a rasteroperations stage 580. In an embodiment, the input data 501 comprisescommands that configure the processing units to implement the stages ofthe graphics processing pipeline 500 and geometric primitives (e.g.,points, lines, triangles, quads, triangle strips or fans, etc.) to beprocessed by the stages. The output data 502 may comprise pixel data(i.e., color data) that is copied into a frame buffer or other type ofsurface data structure in a memory.

The data assembly stage 510 receives the input data 501 that specifiesvertex data for high-order surfaces, primitives, or the like. The dataassembly stage 510 collects the vertex data in a temporary storage orqueue, such as by receiving a command from the host processor thatincludes a pointer to a buffer in memory and reading the vertex datafrom the buffer. The vertex data is then transmitted to the vertexshading stage 520 for processing.

The vertex shading stage 520 processes vertex data by performing a setof operations (i.e., a vertex shader or a program) once for each of thevertices. Vertices may be, e.g., specified as a 4-coordinate vector(i.e., <x, y, z, w>) associated with one or more vertex attributes(e.g., color, texture coordinates, surface normal, etc.). The vertexshading stage 520 may manipulate individual vertex attributes such asposition, color, texture coordinates, and the like. In other words, thevertex shading stage 520 performs operations on the vertex coordinatesor other vertex attributes associated with a vertex. Such operationscommonly including lighting operations (i.e., modifying color attributesfor a vertex) and transformation operations (i.e., modifying thecoordinate space for a vertex). For example, vertices may be specifiedusing coordinates in an object-coordinate space, which are transformedby multiplying the coordinates by a matrix that translates thecoordinates from the object-coordinate space into a world space or anormalized-device-coordinate (NCD) space. The vertex shading stage 520generates transformed vertex data that is transmitted to the primitiveassembly stage 530.

The primitive assembly stage 530 collects vertices output by the vertexshading stage 520 and groups the vertices into geometric primitives forprocessing by the geometry shading stage 540. For example, the primitiveassembly stage 530 may be configured to group every three consecutivevertices as a geometric primitive (i.e., a triangle) for transmission tothe geometry shading stage 540. In some embodiments, specific verticesmay be reused for consecutive geometric primitives (e.g., twoconsecutive triangles in a triangle strip may share two vertices). Theprimitive assembly stage 530 transmits geometric primitives (i.e., acollection of associated vertices) to the geometry shading stage 540.

The geometry shading stage 540 processes geometric primitives byperforming a set of operations (i.e., a geometry shader or program) onthe geometric primitives. Tessellation operations may generate one ormore geometric primitives from each geometric primitive. In other words,the geometry shading stage 540 may subdivide each geometric primitiveinto a finer mesh of two or more geometric primitives for processing bythe rest of the graphics processing pipeline 500. The geometry shadingstage 540 transmits geometric primitives to the viewport SCC stage 550.

In an embodiment, the graphics processing pipeline 500 may operatewithin a streaming multiprocessor and the vertex shading stage 520, theprimitive assembly stage 530, the geometry shading stage 540, thefragment shading stage 570, and/or hardware/software associatedtherewith, may sequentially perform processing operations. Once thesequential processing operations are complete, in an embodiment, theviewport SCC stage 550 may utilize the data. In an embodiment, primitivedata processed by one or more of the stages in the graphics processingpipeline 500 may be written to a cache (e.g. L1 cache, a vertex cache,etc.). In this case, in an embodiment, the viewport SCC stage 550 mayaccess the data in the cache. In an embodiment, the viewport SCC stage550 and the rasterization stage 560 are implemented as fixed functioncircuitry.

The viewport SCC stage 550 performs viewport scaling, culling, andclipping of the geometric primitives. Each surface being rendered to isassociated with an abstract camera position. The camera positionrepresents a location of a viewer looking at the scene and defines aviewing frustum that encloses the objects of the scene. The viewingfrustum may include a viewing plane, a rear plane, and four clippingplanes. Any geometric primitive entirely outside of the viewing frustummay be culled (i.e., discarded) because the geometric primitive will notcontribute to the final rendered scene. Any geometric primitive that ispartially inside the viewing frustum and partially outside the viewingfrustum may be clipped (i.e., transformed into a new geometric primitivethat is enclosed within the viewing frustum. Furthermore, geometricprimitives may each be scaled based on a depth of the viewing frustum.All potentially visible geometric primitives are then transmitted to therasterization stage 560.

The rasterization stage 560 converts the 3D geometric primitives into 2Dfragments (e.g. capable of being utilized for display, etc.). Therasterization stage 560 may be configured to utilize the vertices of thegeometric primitives to setup a set of plane equations from whichvarious attributes can be interpolated. The rasterization stage 560 mayalso compute a coverage mask for a plurality of pixels that indicateswhether one or more sample locations for the pixel intercept thegeometric primitive. In an embodiment, z-testing may also be performedto determine if the geometric primitive is occluded by other geometricprimitives that have already been rasterized. The rasterization stage560 generates fragment data (i.e., interpolated vertex attributesassociated with a particular sample location for each covered pixel)that are transmitted to the fragment shading stage 570.

The fragment shading stage 570 processes fragment data by performing aset of operations (i.e., a fragment shader or a program) on each of thefragments. The fragment shading stage 570 may generate pixel data (i.e.,color values) for the fragment such as by performing lighting operationsor sampling texture maps using interpolated texture coordinates for thefragment. The fragment shading stage 570 generates pixel data that istransmitted to the raster operations stage 580.

The raster operations stage 580 may perform various operations on thepixel data such as performing alpha tests, stencil tests, and blendingthe pixel data with other pixel data corresponding to other fragmentsassociated with the pixel. When the raster operations stage 580 hasfinished processing the pixel data (i.e., the output data 502), thepixel data may be written to a render target such as a frame buffer, acolor buffer, or the like.

It will be appreciated that one or more additional stages may beincluded in the graphics processing pipeline 500 in addition to or inlieu of one or more of the stages described above. Variousimplementations of the abstract graphics processing pipeline mayimplement different stages. Furthermore, one or more of the stagesdescribed above may be excluded from the graphics processing pipeline insome embodiments (such as the geometry shading stage 540). Other typesof graphics processing pipelines are contemplated as being within thescope of the present disclosure. Furthermore, any of the stages of thegraphics processing pipeline 500 may be implemented by one or morededicated hardware units within a graphics processor such as PPU 200.Other stages of the graphics processing pipeline 500 may be implementedby programmable hardware units such as the SM 340 of the PPU 200.

The graphics processing pipeline 500 may be implemented via anapplication executed by a host processor, such as a CPU. In anembodiment, a device driver may implement an application programminginterface (API) that defines various functions that can be utilized byan application in order to generate graphical data for display. Thedevice driver is a software program that includes a plurality ofinstructions that control the operation of the PPU 200. The API providesan abstraction for a programmer that lets a programmer utilizespecialized graphics hardware, such as the PPU 200, to generate thegraphical data without requiring the programmer to utilize the specificinstruction set for the PPU 200. The application may include an API callthat is routed to the device driver for the PPU 200. The device driverinterprets the API call and performs various operations to respond tothe API call. In some instances, the device driver may performoperations by executing instructions on the CPU. In other instances, thedevice driver may perform operations, at least in part, by launchingoperations on the PPU 200 utilizing an input/output interface betweenthe CPU and the PPU 200. In an embodiment, the device driver isconfigured to implement the graphics processing pipeline 500 utilizingthe hardware of the PPU 200.

Various programs may be executed within the PPU 200 in order toimplement the various stages of the graphics processing pipeline 500.For example, the device driver may launch a kernel on the PPU 200 toperform the vertex shading stage 520 on one SM 340 (or multiple SMs340). The device driver (or the initial kernel executed by the PPU 300)may also launch other kernels on the PPU 300 to perform other stages ofthe graphics processing pipeline 500, such as the geometry shading stage540 and the fragment shading stage 570. In addition, some of the stagesof the graphics processing pipeline 500 may be implemented on fixed unithardware such as a rasterizer or a data assembler implemented within thePPU 300. It will be appreciated that results from one kernel may beprocessed by one or more intervening fixed function hardware unitsbefore being processed by a subsequent kernel on an SM 340.

Machine Learning

Deep neural networks (DNNs) developed on processors, such as the PPU 200have been used for diverse use cases, from self-driving cars to fasterdrug development, from automatic image captioning in online imagedatabases to smart real-time language translation in video chatapplications. Deep learning is a technique that models the neurallearning process of the human brain, continually learning, continuallygetting smarter, and delivering more accurate results more quickly overtime. A child is initially taught by an adult to correctly identify andclassify various shapes, eventually being able to identify shapeswithout any coaching. Similarly, a deep learning or neural learningsystem needs to be trained in object recognition and classification forit get smarter and more efficient at identifying basic objects, occludedobjects, etc., while also assigning context to objects.

At the simplest level, neurons in the human brain look at various inputsthat are received, importance levels are assigned to each of theseinputs, and output is passed on to other neurons to act upon. Anartificial neuron or perceptron is the most basic model of a neuralnetwork. In one example, a perceptron may receive one or more inputsthat represent various features of an object that the perceptron isbeing trained to recognize and classify, and each of these features isassigned a certain weight based on the importance of that feature indefining the shape of an object.

A deep neural network (DNN) model includes multiple layers of manyconnected perceptrons (e.g., nodes) that can be trained with enormousamounts of input data to quickly solve complex problems with highaccuracy. In one example, a first layer of the DLL model breaks down aninput image of an automobile into various sections and looks for basicpatterns such as lines and angles. The second layer assembles the linesto look for higher level patterns such as wheels, windshields, andmirrors. The next layer identifies the type of vehicle, and the finalfew layers generate a label for the input image, identifying the modelof a specific automobile brand.

Once the DNN is trained, the DNN can be deployed and used to identifyand classify objects or patterns in a process known as inference.Examples of inference (the process through which a DNN extracts usefulinformation from a given input) include identifying handwritten numberson checks deposited into ATM machines, identifying images of friends inphotos, delivering movie recommendations to over fifty million users,identifying and classifying different types of automobiles, pedestrians,and road hazards in driverless cars, or translating human speech inreal-time.

During training, data flows through the DNN in a forward propagationphase until a prediction is produced that indicates a labelcorresponding to the input. If the neural network does not correctlylabel the input, then errors between the correct label and the predictedlabel are analyzed, and the weights are adjusted for each feature duringa backward propagation phase until the DNN correctly labels the inputand other inputs in a training dataset. Training complex neural networksrequires massive amounts of parallel computing performance, includingfloating-point multiplications and additions that are supported by thePPU 200. Inferencing is less compute-intensive than training, being alatency-sensitive process where a trained neural network is applied tonew inputs it has not seen before to classify images, translate speech,and generally infer new information.

Neural networks rely heavily on matrix math operations, and complexmulti-layered networks require tremendous amounts of floating-pointperformance and bandwidth for both efficiency and speed. With thousandsof processing cores, optimized for matrix math operations, anddelivering tens to hundreds of TFLOPS of performance, the PPU 200 is acomputing platform capable of delivering performance required for deepneural network-based artificial intelligence and machine learningapplications.

Real-Time Ray-Traced Water Surface Caustics

FIG. 6 illustrates a flowchart of a method 600 for implementingreal-time ray-traced water surface caustics, in accordance with anembodiment. Although method 600 is described in the context of aprocessing unit, the method 600 may also be performed by a program,custom circuitry, or by a combination of custom circuitry and a program.For example, the method 600 may be executed by a GPU (graphicsprocessing unit), CPU (central processing unit), or any processorcapable of performing parallel path space filtering by hashing.Furthermore, persons of ordinary skill in the art will understand thatany system that performs method 600 is within the scope and spirit ofembodiments of the present invention.

As shown in operation 602, a water mesh is computed for a scene to berendered. In one embodiment, the water mesh may be a lighting mesh thatincludes a refracted or reflected mesh. For example, the lighting meshmay represent a mesh formed by refraction and/or reflection. In anotherembodiment, a water surface mesh may be determined for a scene to berendered. In yet another embodiment, a ray may be determined for eachvertex of the water surface mesh. In still another embodiment, the watermesh may include a refracted water mesh that is computed utilizingrefracted rays for each vertex of the water surface mesh. In anotherembodiment, the water mesh may include a reflected water mesh that iscomputed utilizing reflected rays for each vertex of the water surfacemesh.

Additionally, as shown in operation 604, light rays are projected fromone or more polygons of a water surface mesh onto geometry of the scene,based on a relationship between the water surface mesh and the watermesh. In one embodiment, a compression ratio may be determined for eachpolygon of the water surface mesh. In another embodiment, light rays maybe projected from one or more polygons of the water surface mesh ontoscene geometry, based on the compression ratio computed for each polygonof the water surface mesh.

Further, as shown in operation 606, lighting of the geometry of thescene is performed, utilizing the projected light rays. In oneembodiment, the light rays may include reflected light rays that areprojected from one or more polygons of a water surface mesh ontoabove-water geometry of the scene, and lighting of the above-watergeometry of the scene may be performed, utilizing the projectedreflected light rays. In another embodiment, the light rays may includerefracted light rays that are projected from one or more polygons of awater surface mesh onto underwater geometry of the scene, and lightingof the underwater geometry of the scene may be performed, utilizing theprojected light rays.

In this way, a refracted water mesh may be used as a guiding mesh todetermine a number and location of refracted or reflected rays to beprojected/generated from a corresponding water surface mesh of a scene.Additionally, refracted or reflected rays may be projected directly froma water surface mesh, instead of from a light source.

In yet another embodiment, water mesh may be computed, light rays may beprojected, and lighting of the geometry of the scene may be performedutilizing a parallel processing unit (PPU) such as the PPU 200illustrated in FIG. 2.

In one embodiment, a real-time raytracing application programminginterface (API) may be used to simplify and innovate on current methodsfor rendering real-time water surface caustics. It may be assumed thatthe necessary bounding volume acceleration structures have already beenimplemented in a game engine to enable other raytracing-based algorithmslike raytraced shadows. If desired, the algorithms described below canalso be used to render caustics from light that gets reflected by thewater surface (e.g., reflected light), as well as refracted light.

The use of the API may have several benefits over existing solutionswith regards to finding the intersections of refracted light rays and adynamic underwater three-dimensional (3D) scene. This is depicted in theexemplary scene 700 in FIG. 7—the light rays 702 from the light source704 interact with the water surface 706 and turn into the refractedlight rays 708 that shed light on the underwater geometry 710.

Many games shy away from finding intersections with the full game scene,but only compute intersections with a ground plane or the inside of a 3Dbox. Therefore, the resulting caustics can't hope to render shadows thatare the result of many incoherent refracted light rays. Typically,shadows are then generated from a shadow map, which only producesshadows from coherent light rays.

Previous methods for managing refraction need to first render a causticsmap, which is an image that contains the refractive geometry. Forexample, the refractive geometry may include the water surface. However,the method described herein doesn't need this intermediate renderingstep. Instead, the ray generation shader directly generates refractedrays on the triangles of the water surface. This conceptually moves theapproach described below more towards photon mapping.

Exemplary Algorithm Overview

In one embodiment, the following steps may be used to render raytracedwater caustics. In a first step, a refracted water mesh may be computed.For example, for each vertex of the water mesh that represents thegeometry of the simulated water surface, a refracted ray R isconstructed. This ray starts at the current position of the water vertexand points along the refracted direction of incident light. Therefracted water mesh has the same number of vertices and the sametriangle count as the water surface. The positions of its vertices arecomputed by intersecting each ray R with the underwater geometry.

FIG. 8 depicts this an example 800 of this process. As shown, everywater surface triangle 802 generates a corresponding triangle 804 in therefracted water mesh. Please note that the refracted water mesh does notneed to be fine enough to follow every detail of the underwatergeometry. It needs to only be detailed enough to facilitate thecomputation of a high enough quality compression ratio as describedbelow. This step can introduce an error when the water surface is notdetailed enough. It is therefore necessary to refine the water surfaceif errors are detected.

Additionally, in a second step, a compression ratio is computed for eachwater triangle. For example, FIG. 9 shows an exemplary refractionexample 900, according to one embodiment. As shown in FIG. 9, therefractions 902 of the light rays 904 can either focus the light withina narrowing triangular beam 906, or can diffuse the light with anexpanding triangular beam 908. As a result, triangles in the refractedwater mesh can either have a bigger or a smaller area than theirrespective water triangle.

In one embodiment, for each triangle the compression ratio is computedas follows and stored in a buffer:

${{compression}\mspace{14mu}{ratio}} = \frac{{area}({WaterTriangle})}{{area}\left( {RefractedWaterTriangle} \right.}$

Further, in a third step, refracted light rays may be generated atrandom locations on the water triangle. For example, for each watertriangle, several random world space positions (e.g., samples, etc.) aregenerated in the triangle. The higher the compression ratio, the moresamples are generated. The algorithm to find an adequate sample countfor a given compression ratio also considers the on-screen size of therefracted triangle. This means that more samples get generated fortriangles that are closer to the viewer.

For each random world space position that can be seen from the lightsource, a ray (photon) is formed starting at the random position andmoving along the interpolated refracted direction. One easy solution tofind out if a sample is shadowed (can't be seen by the light source) isto use a shadow map. It is of course also possible to shoot a raytowards the light source. The intersection of each such ray with theunderwater scene geometry is then computed.

Each intersection is then projected to screen space. For example, if theposition is on-screen, InterlockedAdd( ) may be used to accumulate abrightness value in that screen location. The brightness value that getsaccumulated can be scaled by a number of factors, including thecompression ratio and/or the amount of light that has been absorbed bythe length of the way the ray travels through the water.

FIG. 10 illustrates an exemplary generation 1000 of samples 1002 andtheir corresponding refracted screen space positions 1004, according toone embodiment. It is possible to skip the generation of samples forwater triangles that are guaranteed not to generate any on screenintersections.

Further still, in a fourth step, the buffer resulting from thegeneration of the refracted light rays may be denoised to create adenoised and smooth caustics buffer. In a fifth step, the causticsbuffer may be used to shed light onto the underwater scene.

Exemplary Implementation

In one embodiment, a DirectX12™ DXR may be used to implement all raytracing workloads for the first and third steps above. For the firststep, DispatchRays( ) is called in a way that each thread traces exactlyone refracted ray into the scene. The resulting refracted water mesh iswritten to a buffer that is read by later steps and uses the same indexbuffer as the original water mesh.

The second step is implemented as a compute shader. For the third step,DispatchRays( ) is called with enough threads to be able to cast tracethe maximum number of rays for every water triangle within an enlargedview frustum. The frustum is enlarged to also capture refracted raysthat enter the view frustum via from outside the normal view frustum.The ray generation shader culls (e.g. doesn't call TraceRay( )) if agiven thread has no sample to process.

As depicted in Table 1, a simple seed based random number generator isused to generate a set of ‘random’ barycentric positions inside thecurrent water triangle, according to one embodiment.

TABLE 1 float3 RandBarycentrics(inout uint RandSeed) { float s =RandFloat(RandSeed); float t = RandFloat(RandSeed); [flatten]if (s + t >1.0f) s = 1.0f − s, t = 1.0f − t; return float3(1.0f − s − t, s, t); }

One exemplary implementation uses the triangle ID/index as the RandSeed.This choice means that the generated noise is stable across a triangle.Should the number of samples for a triangle change between frames thenthis does only result in removing or adding samples but never in achange of sample positions for a given triangle.

As described above, the number of samples that is generated is alsobased on the screen space size of the triangle of the refracted watermesh. As this refracted triangle may be off the screen even if some ofthe generated rays produce on screen caustics, the maximum screen spacesize of the refracted triangle and three additional triangles is used.

FIG. 11 illustrates a depiction 1100 of three triangles 1102A-C that getformed at the three different intersection points that the threevertices/rays that originate from the water surface generate. As shownin FIG. 11, the surface triangle 1104 is the triangle at the watersurface, and the three rays 1106A-C show scene intersections at verydifferent distances.

In one embodiment, to speed up the fourth step above, the bufferaccumulating brightness is implemented as a half-res buffer. Thisaccelerates denoising significantly. Denoising is done through a set ofiterated cross-bilateral blurring steps that account for differences inview-space depth, normal and view-space positions.

In one embodiment, regarding multi-bounce caustics, with DXR it ispossible to generate one or more secondary rays in the ray generationshader. In this case for each secondary ray versus intersection, it maybe necessary to accumulate brightness at the projected screen spaceposition of the intersection.

In another embodiment, regarding volumetric caustics, volumetriccaustics may be implemented based on the random ray samples that theabove implementations use (e.g., instead of a caustics map, etc.).

Importance Sampled Ray-Traced Real-Time Caustics

In one embodiment, a mesh may be placed in front of the light or aroundthe light for an omnidirectional light. This mesh may be tessellated toa sufficient degree and may be refracted through the transparent partsof the scene. For example, a water mesh may be used. Note that thedescribed method is not limited to water and can perform multiplebounces.

In one embodiment, a refracted mesh is computed, using ray tracing tofind vertices in the scene. This is the refracted water surface or atessellated mesh in front or around the light source. In anotherembodiment, a ratio of the areas of the original water triangle and therefracted triangle is computed.

If the refracted triangle is smaller and thus brighter, random pointsare generated on the water triangle. Rays are traced from random pointsalong refracted light directions. Brightness to the screen is determinedat intersection points with the scene. Noisy caustics are denoised andused to light the (underwater) scene.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Thus, the breadth and scope of a preferred embodiment shouldnot be limited by any of the above-described exemplary embodiments, butshould be defined only in accordance with the following claims and theirequivalents.

What is claimed is:
 1. A method comprising: determining a water surfacemesh for a scene to be rendered, the water surface mesh being a polygonmesh representing a water surface within the scene; determining a rayfor one or more vertices of the water surface mesh, the ray being atleast one of a refracted ray that points along a refracted direction ofincident light or a reflected ray that points along a reflecteddirection of incident light; computing a lighting mesh that is at leastone of: a reflected lighting mesh for the scene to be rendered, wherepositions of one or more vertices within the reflected lighting mesh aredetermined by intersecting each reflected ray with above-water geometryin the scene to be rendered, or a refracted lighting mesh for the sceneto be rendered, where positions of one or more vertices within therefracted lighting mesh are determined by intersecting each refractedray with below-water geometry in the scene to be rendered; determining,based on a calculated relationship between the water surface mesh andthe lighting mesh, a number of light rays to be projected from the watersurface mesh and locations on the water surface mesh from which toproject the light rays; projecting the determined number of light raysthe determined locations on the water surface mesh onto geometry of thescene; and performing lighting of the geometry of the scene, utilizingthe projected light rays.
 2. The method of claim 1, wherein the numberof light rays projected from one or more polygons of the water surfacemesh is based on an on-screen size of corresponding polygons within thelighting mesh.
 3. The method of claim 1, wherein the determinedlocations from which to project the light rays include a determined oneor more polygons of the water surface mesh, and wherein the light raysare projected from random positions within each polygon of thedetermined one or more polygons of the water surface mesh.
 4. The methodof claim 1, further comprising: determining, for each polygon of thewater surface mesh for which refracted light rays are to be projected,an intersection of each projected light ray with underwater scenegeometry, and projecting each intersection to a screen space location.5. The method of claim 4, further comprising accumulating a brightnessvalue for the screen space location in a buffer in response todetermining that the screen space location is on-screen.
 6. The methodof claim 1, further comprising: determining, for each polygon of thewater surface mesh for which reflected light rays are to be projected,an intersection of each projected light ray with above-water scenegeometry, and projecting each intersection to a screen space location.7. The method of claim 6, further comprising accumulating a brightnessvalue for the screen space location in a buffer in response todetermining that the screen space location is on-screen.
 8. The methodof claim 1, wherein the lighting mesh is the refracted lighting mesh,and the light rays are refracted light rays projected from the watersurface mesh onto underwater geometry of the scene.
 9. The method ofclaim 1, wherein the lighting mesh is the reflected lighting mesh, andthe light rays are reflected light rays projected from the water surfacemesh onto above-water geometry of the scene.
 10. The method of claim 1,wherein each polygon of the water surface mesh corresponds to a polygonof the lighting mesh, and wherein determining a number of light rays tobe projected from the water surface mesh and locations on the watersurface mesh from which to project the light rays is performedindependently for each polygon of the water surface mesh, based on acalculated relationship between the polygon of the water surface meshand the corresponding polygon of the lighting mesh.
 11. The method ofclaim 10, wherein the calculated relationship between the polygon of thewater surface mesh and the corresponding polygon of the lighting meshincludes a compression ratio between the polygon of the water surfacemesh and the corresponding polygon of the lighting mesh.
 12. The methodof claim 11, wherein polygons of the water surface mesh with acompression ratio less than a predefined threshold have a lower numberof light rays projected therefrom than polygons of the water surfacemesh with a compression ratio that exceeds the predefined threshold. 13.A system comprising: a processor that is configured to: determine awater surface mesh for a scene to be rendered, the water surface meshbeing a polygon mesh representing a water surface within the scene;determine a ray for one or more vertices of the water surface mesh, theray being at least one of a refracted ray that points along a refracteddirection of incident light or a reflected ray that points along areflected direction of incident light; compute a lighting mesh that isat least one of: a reflected lighting mesh for the scene to be rendered,where positions of one or more vertices within the reflected lightingmesh are determined by intersecting each reflected ray with above-watergeometry in the scene to be rendered, or a refracted lighting mesh forthe scene to be rendered, where positions of one or more vertices withinthe refracted lighting mesh are determined by intersecting eachrefracted ray with below-water geometry in the scene to be rendered;determine, based on a calculated relationship between the water surfacemesh and the lighting mesh, a number of light rays to be projected fromthe water surface mesh and locations on the water surface mesh fromwhich to project the light rays; project the determined number of lightrays from the determined locations on the water surface mesh ontogeometry of the scene; and perform lighting of the geometry of thescene, utilizing the projected light rays.
 14. A method comprising:determining a water surface mesh for a scene to be rendered, the watersurface mesh being a polygon mesh representing a water surface withinthe scene; for each vertex of the water surface mesh, determining arefracted ray that points along a refracted direction of incident light;computing a refracted lighting mesh for the scene, utilizing therefracted rays where positions of one or more vertices within therefracted lighting mesh are determined by intersecting each refractedray with below-water geometry in the scene to be rendered; computing acompression ratio for each polygon of the water surface mesh, thecompression ratio being between the polygon of the water surface meshand a corresponding polygon of the refracted lighting mesh; determining,based on the compression ratio computed for each polygon of the watersurface mesh, a number of refracted light rays to be projected from thewater surface mesh and one or more polygons of the water surface meshfrom which to project the refracted light rays,; projecting thedetermined number of refracted light rays from the determined one ormore polygons of the water surface mesh onto underwater scene geometry;and performing lighting of the underwater scene geometry, utilizing theprojected refracted light rays.